This mathematics lesson defines even and odd numbers and explores properties of adding and multiplying even and odd numbers. It states that the sum of two even numbers or two odd numbers is even or odd respectively. The sum of an even and odd number is odd. When multiplying, the product of two even numbers is even, two odd numbers is odd, and an even and odd number is even. Students are given examples and exercises to practice identifying whether sums and products are even or odd.

1. Lesson 16
NYS COMMON CORE MATHEMATICS CURRICULUM
6•2
Lesson 16:Even and Odd Numbers
Classwork
Opening Exercise
What is an even number?
List some examples of even numbers.
What is an odd number?
List some examples of odd numbers.
What happens when we add two even numbers? Will we always get an even number?
Lesson 16:
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2. Lesson 16
NYS COMMON CORE MATHEMATICS CURRICULUM
6•2
Exercises
1.
Why is the sum of two even numbers even?
a.
b.
Circle pairs of dots to determine if any of the dots are left over.
c.
2.
Think of the problem
. Draw dots to represent each number.
Will this be true every time two even numbers are added together? Why or why not?
Why is the sum of two odd numbers even?
a.
Think of the problem
b.
Circle pairs of dots to determine if any of the dots are left over.
c.
Will this be true every time two odd numbers are added together? Why or why not?
Lesson 16:
Date:
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. Draw dots to represent each number.
Even and Odd Numbers
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3. Lesson 16
NYS COMMON CORE MATHEMATICS CURRICULUM
3.
6•2
Why is the sum of an even number and an odd number odd?
a.
Think of the problem
. Draw dots to represent each number.
b.
Circle pairs of dots to determine if any of the dots are left over.
c.
Will this be true every tie an even number and an odd number are added together? Why or why not?
d.
What if the first addend was odd and the second was even. Would the sum still be odd? Why or why not? For
example, if we had
, would the sum be odd?
Let’s sum it up:



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4. NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 16
6•2
Exploratory Challenge
Each group will determine on its poster paper whether one of the following products is odd or even: The product of two
even numbers, the product of two odd numbers, or the product of an even number and an odd number. Use previous
knowledge about even and odd numbers, the connection between addition and multiplication, and visual methods (e.g.,
dots) in your proofs.
1.
The product of two even numbers is even.
2.
The product of two odd numbers is odd.
3.
The product of an even number and an odd number is even.
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Even and Odd Numbers
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5. Lesson 16
NYS COMMON CORE MATHEMATICS CURRICULUM
6•2
Lesson Summary
Adding:

The sum of two even numbers is even.

The sum of two odd numbers is odd.

The sum of an even number and an odd number is odd.
Multiplying:

The product of two even numbers is even.

The product of two odd numbers is odd.

The product of an even number and an odd number is even.
Problem Set
Tell whether each sum or product is even or odd. Explain your reasoning.
1.
2.
3.
4.
5.
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Date:
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Even and Odd Numbers
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